An infant\'s toy has a 120 g wooden animal hanging from a spring. If pulled down

Question

An infant's toy has a 120 g wooden animal hanging from a spring. If pulled down gently, the animal oscillates up and down with a period of 0.47 s . His older sister pulls the spring a bit more than intended. She pulls the animal 25 cm below its equilibrium position, then lets go. The animal flies upward and detaches from the spring right at the animal's equilibrium position.

If the animal does not hit anything on the way up, how far above its equilibrium position will it go? (Express your answer to two significant figures and include the appropriate units.)

h=___________

Explanation / Answer

formula for period of spring oscillator is

T = 2pi sqrt m/k

k = 4 pi^2 m/T^2

= 4 pi^2 (0.120)/0.47)^2

= 21.44 N/m

Apply conservation of energy

1/2 kx^2 = 1/2 mv^2

v = x sqrt k/m= 0.24sqrt 21.44/0.120

=3.2 m/s

Apply kinematic equation

V^2 - v^2 = 2 ah

0-(3.2)^2 = 2 (-9.8) h

h = 0.525 m

rounding to two significant digits

h = 0.52 m

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